Generalizations of Hermite-Hadamard, Bullen and Simpson inequalities via h−convexity

[1] M. U. Awan, N. Akhtar, S. Iftikhar, et al., New Hermite Hadamard type inequalities for n-polynomial harmonically convex functions, J. Inequal. Appl., vol. 125, 2020. https://doi.org/10.1186/s13660-020-02393-x Search in Google Scholar

[2] W. W. Breckner, Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Raumen, Pupl. Inst. Math., vol. 23, 1978, 13-20. Search in Google Scholar

[3] W. W. Breckner, Continuity of generalized convex and generalized concave set-valued functions, Rev Anal. Numer. Thkor. Approx., vol. 22, 1993, 39-51. Search in Google Scholar

[4] S. S. Dragomir, J. Pečarić, L. E. Persson, Some inequalities of Hadamard type, Soochow J. Math., vol. 21, 1995, 335-241. Search in Google Scholar

[5] S. S. Dragomir, R. P. Agarwal, P. Cerone, On Simpson’s inequality and applications, J. Inequal. Appl., vol. 5, no. 6, 2000, 533-579. Available online at http://dx.doi.org/10.1155/S102558340000031X. Search in Google Scholar

[6] E. K. Godunova, V. I. Levin, Neravenstva dlja funkcii sirokogo klassa, soderzascego vypuklye, monotonnye i nekotorye drugie vidy funkii, Vycislitel, Mat. i. Fiz. Mezvuzov. Sb. Nauc. Trudov, MGPI, Moskva, 1985, 138-142. Search in Google Scholar

[7] H. Hudzik, L. Maligranda, Some remarks on s−convex functions, Aequationes Math., vol. 48, 1994, 100-111. Search in Google Scholar

[8] D. S. Mitrinović, J. Pečarić, A. M. Fink, Classical and new inequalities in analysis, KluwerAcademic, Dordrecht, 1993. Search in Google Scholar

[9] M. Bombardelli, S. Varošanec, Properties of h−convex functions related to the Hermite-Hadamard-Fejér inequalities, Comput. Math. Appl., vol. 58, 2009, 1869-1877. Search in Google Scholar

[10] M. Z. Sarıkaya, A. Sağlam, H. Yıldırım, On some Hadamard-type inequalities for h−convex functions, J. Math. Inequal., vol. 2, no. 3, 2008, 335-341. Search in Google Scholar

[11] M. Z. Sarıkaya, E. Set, M. E.Özdemir, On some new inequalities of Hadamard-type involving h−convex functions, Acta Math. Univ. Comenian LXXIX, no. 2, 2010, 265-272. Search in Google Scholar

[12] M. E.Özdemir, M. Gürbüz, A. O. Akdemir, Inequalities for h−Convex Functions via Further Properties, RGMIA Research Report Collection, vol. 14, article 22, 2011. Search in Google Scholar

[13] M. Bessenyei, The Hermite-Hadamard inequality on simplices, Amer. Math. Monthly, vol. 115, no. 4, 2008, 339-345. MR 2009b:52023 Search in Google Scholar

[14] M. Bessenyei, Hermite-Hadamard-type inequalities for generalized convex functions, J. Inequal. Pure Appl. Math., vol. 9, no. 3, 2008, Article 63, pp. 51 (electronic). Search in Google Scholar

[15] M. Bessenyei, The Hermite-Hadamard inequality in Beckenbach’s setting, J. Math. Anal. Appl., vol. 364, no. 2, 2010, 366-383. MR2576189 Search in Google Scholar

[16] P. Burai, A. Házy, On Orlicz-convex functions, Proc. 12th Symp. Math. Appl. (November 5-7, 2009, University of Timioara), Editura Politechnica, 2010, 73-79. Search in Google Scholar

[17] P. Burai, A. Házy, On approximately h−convex functions, J. Convex Anal., vol. 18, no. 2, 2011, 447-454. Search in Google Scholar

[18] P. Burai, A. Házy, T. Juhász, Bernstein-Doetsch type results for s−convex functions, Publ. Math. Debrecen, vol. 75, no. 1-2, 2009, 23-31. Search in Google Scholar

[19] P. Burai, A. Házy, T. Juhász, On approximately Breckner s−convex functions, Control Cybernet., vol. 40, no. 1, 2011, 91-99. Search in Google Scholar

[20] M. Bessenyei, Zs. Páles, Higher-order generalizations of Hadamard’s inequality, Publ. Math. Debrecen, vol. 61, no. 3-4, 2002, 623-643. MR 2003k:26021 Search in Google Scholar

[21] M. Bessenyei, Zs. Páles, Characterizations of convexity via Hadamard’s inequality, Math. Inequal. Appl., vol. 9, no. 1, 2006, 53-62. MR 2007a:26010 Search in Google Scholar

[22] A. Házy, Bernstein-Doetsch type results for h−convex functions, Math. Inequal. Appl., vol. 14, no. 3, 2011, 499-508. Search in Google Scholar

[23] S. Hussain, J. Khalid, Y.-M. Chu, Some generalized fractional integral Simpson’s type inequalities with applications, J. AIMS Mathematics, vol. 5, no. 6, 2020, 5859-5883. doi: 10.3934/math.2020375 Search in Google Scholar

[24] M. A. Khan, A. Iqbal, M. Suleman, Y.-M. Chu, Hermite-Hadamard type inequalities for fractional integrals via Green’s function, J. Inequal. Appl., vol. 161, 2018. https://doi.org/10.1186/s13660-018-1751-6 Search in Google Scholar

[25] Y. Khurshid, M. A. Khan, Y.-M. Chu, Conformable integral version of Hermite-Hadamard-Fejér inequalities via η−convex functions, J. AIMS Mathematics, vol. 5, no. 5, 2020, 5106-5120. doi: 10.3934/math.2020328 Search in Google Scholar

[26] B. G. Pachpatte, Mathematical Inequalities, North-Holland Mathematical Library, Elsevier Science B. V. Amsterdam, 2005. Search in Google Scholar

[27] J. E. Pečarić, F. Proschan, Y. L. Tong, Convex Functions, Partial Orderings and Statistical Applications, Academic Press, 1991. Search in Google Scholar

[28] M. Tunç, Some Hadamard-Like Inequalities via Convex and s−Convex Functions and their Applications for Special Means, Mediterr. J. Math., vol. 11, 2014, 1047. https://doi.org/10.1007/s00009-013-0373-y Search in Google Scholar

[29] M. Tunç, On new inequalities for h−convex functions via Riemann-Liouville fractional integration, Filomat, vol. 27, no. 4, 2013, 559-565. Search in Google Scholar

[30] S. Varošanec, On h−convexity, J. Math. Anal. Appl., vol. 326, no. 1, 2007, 303-311. Search in Google Scholar

[31] P. Yan, Qi Li, Y.-M. Chu, S. Mukhtar, S. Waheed, On some fractional integral inequalities for generalized strongly modified h−convex functions, J. AIMS Mathematics, vol. 5, no. 6, 2020, 6620-6638. doi: 10.3934/math.2020426 Search in Google Scholar

[32] S.-S. Zhou, S. Rashid, M. A. Noor, K. I. Noor, F. Safdar, Y.-M. Chu, New Hermite-Hadamard type inequalities for exponentially convex functions and applications, J. AIMS Mathematics, vol. 5, no. 6, 2020, 6874-6901. doi: 10.3934/math.2020441 Search in Google Scholar